Level Statistics and Localization for Two Interacting Particles in a Random Potential

We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define the symmetry breaking parameter $\mu \propto U^{-2}$ associated to the statistical invariance under change of basis. We show that the Wigner-Dyson rigidity of the energy levels is maintained up to an energy $E_{\mu}$. We find that $E_{\mu} \propto 1/\sqrt{\mu}$ when $\Gamma$ (the inverse lifetime of the states of the preferential basis) is smaller than $\Delta_2$ (the level spacing), and $E_{\mu} \propto 1/\mu$ when $\Gamma > \Delta_2$. This implies that the two-particle localization length $L_2$ first increases as $|U|$ before eventually behaving as $U^2$.Comment: 4 pages REVTEX, 4 Figures EPS, UUENCODE

Disorder-induced enhancement of the persistent current for strongly interacting electrons in one-dimensional rings

We show that disorder increases the persistent current of a half-filled one-dimensional Hubbard-Anderson ring at strong interaction. This unexpected effect results from a perturbative expansion starting from the strongly interacting Mott insulator ground state. The analytical result is confirmed and extended by numerical calculations.Comment: 7 pages, 2 figures, LaTeX, using epl.cls (included), considerably revised final versio

Signatures of electron correlations in the transport properties of quantum dots

The transition matrix elements between the correlated $N$ and $N\!+\!1$ electron states of a quantum dot are calculated by numerical diagonalization. They are the central ingredient for the linear and non--linear transport properties which we compute using a rate equation. The experimentally observed variations in the heights of the linear conductance peaks can be explained. The knowledge of the matrix elements as well as the stationary populations of the states allows to assign the features observed in the non--linear transport spectroscopy to certain transition and contains valuable information about the correlated electron states.Comment: 4 pages (revtex,27kB) + 3 figures in one file ziped and uuencoded (postscript,33kB), to appear in Phys.Rev.B as Rapid Communicatio

Modeling Luminosity-Dependent Galaxy Clustering Through Cosmic Time

We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model the observed luminosity dependence and evolution of galaxy clustering through most of the age of the universe, from z~5 to z~0. We use a simple, non-parametric model which monotonically relates galaxy luminosities to the maximum circular velocity of dark matter halos (V_max) by preserving the observed galaxy luminosity function in order to match the halos in simulations with observed galaxies. The novel feature of the model is the use of the maximum circular velocity at the time of accretion, V_max,acc, for subhalos, the halos located within virial regions of larger halos. We argue that for subhalos in dissipationless simulations, V_max,acc reflects the luminosity and stellar mass of the associated galaxies better than the circular velocity at the epoch of observation, V_max,now. The simulations and our model L-V_max relation predict the shape, amplitude, and luminosity dependence of the two-point correlation function in excellent agreement with the observed galaxy clustering in the SDSS data at z~0 and in the DEEP2 samples at z~1 over the entire probed range of projected separations, 0.1<r_p/(Mpc/h)<10.0. In particular, the small-scale upturn of the correlation function from the power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced very well. At z~3-5, our predictions also match the observed shape and amplitude of the angular two-point correlation function of Lyman-break galaxies (LBGs) on both large and small scales, including the small-scale upturn.Comment: 16 pages 11 figures, ApJ in pres

Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for publication in Phys. Rev.

Quantum Dot as Spin Filter and Spin Memory

We consider a quantum dot in the Coulomb blockade regime weakly coupled to current leads and show that in the presence of a magnetic field the dot acts as an efficient spin-filter (at the single-spin level) which produces a spin-polarized current. Conversely, if the leads are fully spin-polarized the up or down state of the spin on the dot results in a large sequential or small cotunneling current, and thus, together with ESR techniques, the setup can be operated as a single-spin memory.Comment: 4 pages, 3 figures, REVTe

Dependence of the local reionization history on halo mass and environment: did Virgo reionize the Local Group?

The reionization of the Universe has profound effects on the way galaxies form and on their observed properties at later times. Of particular importance is the relative timing of the reionization history of a region and its halo assembly history, which can affect the nature of the first stars formed in that region, the properties and radial distribution of its stellar halo, globular cluster population and its satellite galaxies. We distinguish two basic cases for the reionization of a halo - internal reionization, whereby the stars forming in situ reionize their host galaxy, and external reionization, whereby the progenitor of a galaxy is reionized by external radiation before its own stars are able to form in sufficient numbers. We use a set of large-scale radiative transfer and structure formation simulations, based on cosmologies derived from both Wilkinson Microwave Anisotropy Probe (WMAP) one-year and WMAP three-year data, to evaluate the mean reionization redshifts and the probability of internal/external reionization for Local Group-like systems, galaxies in the field and central cD galaxies in clusters. We find that these probabilities are strongly dependent on the underlying cosmology and the efficiency of photon production, but also on the halo mass. There is a rapid transition between predominantly external and predominantly internal reionization at a mass scale of ∼1012 M⊙ (corresponding roughly to L* galaxies), with haloes less massive than this being reionized preferentially from distant sources. We provide a fit for the reionization redshift as a function of halo mass, which could be helpful to parametrize reionization in semi-analytical models of galaxy formation on cosmological scales. We find no statistical correlation between the reionization history of field galaxies and their environmen

Critical Spectral Statistics at the Metal-Insulator Transition in Interacting Fermionic Systems

The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but strongly depends on the number of particles. At the critical point, we report a substantial decrease of the degree of level repulsion as the number of particles increases indicating a decrease of nearest level correlations associated with the sparsity of the Hamiltonian matrix.Comment: Revtex, 4 pages, 3 encapsulated postscript figures appended Final version as accepted for publication in PR

Galaxy Groups in the SDSS DR4: II. halo occupation statistics

We investigate various halo occupation statistics using a large galaxy group catalogue constructed from the SDSS DR4 with an adaptive halo-based group finder. The conditional luminosity function (CLF) is measured separately for all, red and blue galaxies, as well as in terms of central and satellite galaxies. The CLFs for central and satellite galaxies can be well modelled with a log-normal distribution and a modified Schechter form, respectively. About 85% of the central galaxies and about 80% of the satellite galaxies in halos with masses M_h\ga 10^{14}\msunh are red galaxies. These numbers decrease to 50% and 40%, respectively, in halos with M_h \sim 10^{12}\msunh. For halos of a given mass, the distribution of the luminosities of central galaxies, $L_c$, has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the central galaxies scales with halo mass as $L_c\propto M_h^{0.17}$ ($M_{*,c}\propto M_h^{0.22}$) for halos with masses M\gg 10^{12.5}\msunh, and both relations are significantly steeper for less massive halos. We also measure the luminosity (stellar mass) gap between the first and second brightest (most massive) member galaxies, $\log L_1 - \log L_2$ ($\log M_{*,1}-\log M_{*,2}$). These gap statistics, especially in halos with M_h \la 10^{14.0}\msunh, indicate that the luminosities of central galaxies are clearly distinct from those of their satellites. The fraction of fossil groups, defined as those groups with $\log L_1 - \log L_2\ge 0.8$, ranges from $\sim 2.5$ for groups with M_h\sim 10^{14}\msunh to 18-60% for groups with M_h\sim 10^{13}\msunh. Finally, we measure the fraction of satellites, which changes from $\sim 5.0$ for galaxies with \rmag\sim -22.0 to $\sim40$ for galaxies with \rmag\sim -17.0. (abridged)Comment: 16 pages, 11 figures. Accepted for publication in Ap